NYU is the largest private university in the US, and has bases in Tel Aviv, Buenos Aires and Abu Dhabi among other locations. Photograph: Spencer Platt/Getty Images

An attempt to force out the president of New York University got under way on Monday as a dispute over the institution's grand expansion plans came to a head.

Members of the university's faculty of arts and sciences began a vote of no confidence in John Sexton, who is accused of running NYU with an "excessive use of executive power" more akin to a large corporation than a respected university.

A large number of faculty members are thought to oppose Sexton, but even if he loses the vote, which will be completed on Friday, any decision on his future rests with the board of trustees, which has so far given him strong backing.

Board of trustees chair Martin Lipton said on Monday: "The trustees strongly and unanimously support John. We are mindful of the concerns held by some faculty, but the trustees see a thriving, advancing university.

"We have confidence that John and faculty will continue to work together for the betterment of the university. Positive steps in this direction have already begun."

Under Sexton's tenure, NYU, America's largest private university, has been transformed into a lucrative overseas brand with 10 international centres, including bases in Tel Aviv, Buenos Aires and Abu Dhabi.

The expansion has won praise from Hillary Clinton, who in 2011 lauded Sexton's "vision to expand his university internationally while maintaining its reputation for excellence and academic freedom".

But in New York, many academics voiced doubt about the plans. "Faculty had no say over whether we wanted to be a global university," said Andrew Ross, a sociologist and president of the NYU's chapter of the American Association of University Professors.

He added that the move was solely a decision made by the president and was indicative of the way the university was being run. "It is more akin to executive power used at a corporation. Universities are not supposed to be run like that. They are supposed to be run by shared governance," he told the Guardian.

In particular, concerns have been raised at the locations of some of the overseas centres. Some faculty members have complained that NYU's reputation could be tarnished as a result of human rights abuses in the United Arab Emirates, whose government has donated tens of millions of dollars to NYU.

In a statement on Monday, Sexton said: "Whatever the outcome of this vote, I can say that I have confidence in the NYU faculty – they are an extraordinary scholarly community.

"In the university setting, we believe in criticism, because it makes us better. And when good colleagues have suggestions about how I can improve in serving the university, I listen carefully."

Votes of no confidence in university heads are not unheard of. In November, faculty at the University of San Diego voted in favour of removing its university president. At Kean University in New Jersey, professors and other staff affirmed a lack of confidence in the university's board of trustees.

"It is becoming more common in American universities. It is a last resort of faculty, and a response to administration wielding of executive power," Ross said.

Sexton's management style is not the only issue: a plan to expand its New York City campus, known as NYU 2031, has attracted significant opposition.

Sexton defended the plan in an open letter to New Yorkers. He wrote: "Having been extremely economical with space – NYU has approximately half the square footage per student of Columbia, one quarter of Harvard's – the university has reached a tipping point.

"Space is required to create a vibrant intellectual community in all senses of the phrase, with teachers and learners in proximity to each other, ready and willing to engage with other thinkers and doers throughout the city."

Those behind the confidence vote, however, fear that the president's vision for a larger New York campus will run roughshod over the need to maintain culturally sensitive areas in the city.

"What is planned will transform downtown Manhattan," Ross said. "That has caused concern not just from faculty, but among the community at large in Greenwich Village."

It is unsure just how far the vote could go in unseating Sexton. Ross concedes that the board of trustees are "big supporters" of the president, who has overseen a large injection of new money. Trustees have also awarded him large increases in his salary, which now stands at nearly $1.5m.

But a high-profile "no" vote could go some way to forcing the hands of board members, especially if other schools at NYU initiate their own ballots.

Ross suggested that among other faculties eying a confidence vote were the Tisch school of the arts, the Gallatin achool, and the Steinhardt school of culture, education and human Development.

"Faculty senators are certainly interested in following suit," he added. The faculty of arts and science vote closes Friday at 6pm, with the result expected soon after.